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Resolvent near zero energy on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach

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arxiv 1905.12809 v2 pith:TJZW5R6W submitted 2019-05-30 math.AP

Andras Vasy This is my paper · ORCID
classification math.AP
keywords energylagrangianzeroasymptoticallyconicnearperspectiveresolvent
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We use a Lagrangian regularity perspective to discuss resolvent estimates near zero energy on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. In addition to the Lagrangian perspective we introduce and use a resolved pseudodifferential algebra to deal with zero energy degeneracies in a robust manner.

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  1. Existence and asymptotics of nonlinear Helmholtz eigenfunctions

    math.AP 2019-08 conditional novelty 6.0 of 10

    Small nonlinear Helmholtz equations have solutions with prescribed incoming and outgoing wave patterns at infinity, on Euclidean space and asymptotically conic manifolds, under a dimension-degree condition.

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